An alternative resolution to the Mansuripur paradox

Abstract

In 2013 an article published online by the journal Science declared that the paradox proposed by Masud Mansuripur was resolved. This paradox concerns a point charge-Amperian magnetic dipole system as seen in a frame of reference where they are at rest and one in which they are moving. In the latter frame an electric dipole appears on the magnetic dipole. A torque is then exerted upon the electric dipole by the point charge, a torque that is not observed in the at-rest frame. Mansuripur points out this violates the relativity principle and suggests the Lorentz force responsible for the torque be replaced by the Einstein–Laub force. The resolution of the paradox reported by Science, based on numerous papers in the physics literature, preserves the Lorentz force but depends on the concept of hidden momentum. Here I propose a different resolution based on the overlooked fact that the charge-magnetic dipole system contains linear and angular electromagnetic field momentum. The time rate of change of the field angular–momentum in the frame through which the system is moving cancels that due to the charge-electric dipole interaction. From this point of view hidden momentum is not needed in the resolution of the paradox.